Fluid Flow Analysis in a Concentric Annulus with a

International Journal of Science and Research (IJSR) ISSN: 2319-7064

ResearchGate Impact Factor (2018): 0.28 | SJIF (2019): 7.583

Volume 9 Issue 8, August 2020

www.ijsr.net Licensed Under Creative Commons Attribution CC BY

Fluid Flow Analysis in a Concentric Annulus with a

Rotating Inner Cylinder using ANSYS

M.R. Sahin

1Department of Mechanical Engineering, NERIST, Nirjuli, Arunachal Pradesh, India

Abstract: In the present study, CFD (Computational Fluid Dynamics) analysis of velocity and pressure fields that occur in annular

gap between two concentric cylinders was done. It encompassed the effects of inner cylinder rotation and fluid viscosity on an axial flow

structure. Fluid flow in concentric annuli with and without rotating inner cylinder was investigated by numerical simulation as similar

flows occur in drilling operations of oil wells. So, prediction of flow in drilling pipe in an annular space between wellbore and drill pipe

is essential to determine the variation in fluid pressure within the wellbore. Numerical results obtained for pressure drop and velocity

profiles from the present study were compared with experimental data as well as simulated data from the literature using two non-

Newtonian fluids (0.2 % Xanthan Gum and 0.2 % Carboxymethyl cellulose). The simulated results of pressure drop in present study

showed a good agreement with the experimental data and also yield data that were found rather more inclined towards the simulated

data. The velocity and tangential profiles also showed a good agreement with simulated velocity profiles reported in literature. The

additional work also contained, the study of Newtonian fluid (water) and its effects on hydrodynamics of these annular systems and

compared.

Keywords: Newtonian, Non-Newtonian, Concentric, Annulus, Rotation

1. Introduction

The flow in enclosed space have received much attention

because of many practical technology-driven applications

such as in production of oil & gas, centrifugally-driven

separation processes, electrochemical cells, fluid

viscometers and chemical reactors.

The petroleum industry in particular has shown considerable

interest in studies of fluid dynamics in annular space of oil

drilling operations. A typical example is the case of annular

flow of mud between drill shaft and drilling well casing to

remove cuttings and friction generated heat after drilling

operation. The cut region is cleaned to avoid unnecessary

rise in torque due to accumulation of particles [1]. The flow

of drilling fluid is highly affected by these drag particles

which is determined by velocity profiles in annular region

[2]. Therefore, for efficient drilling operations, knowledge

based on drilling fluid hydraulics is necessary. Moreover, the

rotating inner drill pipe promotes swirling fluid motion that

is superimposed on pressure driven axial flow in bore well

which is maintained axially downstream. In practical field,

pipe rotation drastically decreases frictional pressure loss

inside the wellbores [3]. So, these inner pipe rotations too

have a significant influence on drilling fluid hydraulics and

performance. Moreover drilling muds shows Non-Newtonian

behavior which is complicated to describe in a simple model.

So, proper selection of rheological model is necessary for

calculations to describe drilling fluid rheology.

An experimental study was done on combined axial and

rotational flow in annulus section of rotating inner wall (Fig.

1) [4].They mainly identified the following basic flow

regimes in the annular gap: laminar flow, laminar flow with

vortices, turbulent flow, and turbulent flow with vortices.

The works on flow velocity characteristics of rotating and

non-rotating Newtonian fluids in concentric and eccentric

annuli stands out among experimental studies on turbulent

flow [5]. These authors used Newtonian and Non-Newtonian

fluids to analyze turbulent flow in vertical annular sections

and to determine mean velocity profiles, their fluctuations

and cross-correlation by means of LDV technique (Laser

Doppler Velocimetry).

An extended study on their earlier experimental studies [5]

was done on vertical turbulent flows including the rotational

effects of inner tube [6]. Further, studies on an eccentric

annulus was done and was found that the influence of inner

cylinder rotation is more significant in the range of Reynolds

number (Re < 3000). However, this influence is found to be

lower in turbulent flows.

Figure 1: Schematic representation of different regions of flow

in annulus [4]

Experimental study of Newtonian and pseudoplastic fluid

flow was performed under the influence of central body

rotation by using LDA (Laser Doppler Anemometry) as the

measuring technique [7]. They used glucose syrup solutions

as Newtonian fluid and Carboxymethyl-cellulose (CMC)

solutions as non-Newtonian fluid to plot velocity profiles for

different flow situations and also highlighted the behavior of

the friction factor as a function of fluid flow rate.

Evaluation was done on the flow of pseudoplastic fluids in

eccentric annulus through numerical simulations using finite

difference technique [8]. The effects of inner cylinder

rotation on laminar flow of both Newtonian and Non-

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 1





Newtonian fluids were studied in an eccentric annular

section to compare experimental and numerical results and

also to highlight velocity profiles with those reported by

other authors ([5], [1]) [9].

With rapid improvement of computational resources,

numerical simulation using CFD technique has become very

popular in several fields of Engineering, [10-16] helping to

shed light on the fluid dynamic behavior of annular flows.

The effects of porosity were incorporated at the boundary of

the system into their simulations [17]. They analyzed the

flow to predict pressure loss behavior of drilling fluids which

they later reported with information available in literature,

but did not compare their numerical results with

experimental data. Further, estimation on concentric annular

flows in vertical and horizontal arrangements based on CFD

simulations was done but without the effects of internal shaft

rotation [18]. The above mentioned research are mostly been

focused on experimental and numerical investigations

without comparisons. There is need for studies that combine

both experimental work and CFD simulations to investigate

pressure gradients of different Non- Newtonian fluids in

concentric annuli, evaluating their effects on the

hydrodynamics of these systems. Therefore, this piece of

work was taken by the present author during the Master

degree program (2015-17) at the Institute NERIST (North

Eastern Regional Institute of Engineering and Technology),

Arunachal Pradesh for evaluation and validations.

In the present work, CFD simulations were performed to

evaluate the pressure gradients and flow characteristics in

concentric annuli, with or without inner shaft rotation. The

velocity profiles and pressure drop is analyzed and validated

with standard results reported [19] in annuli with radii ratio

0.45 using two Non-Newtonian fluids involving 0.2%

Xanthan gum and 0.2% Carboxymethyl-cellulose aqueous

solution. In oil and gas drilling operations, the radii ratios of

conventional drilling are supposed to be in range of 0.3-0.5.

Hence radii ratio of 0.45 is selected as they may show the

best flow characteristics of the conventional wellbore

drillings. In addition to the above, the work is extended to

test the Newtonian fluid (i.e., water) to study the pressure

drop and flow characteristics and compared to the results

obtained for aforesaid two Non-Newtonian fluids.

2. Governing equations and Boundary

Conditions

A schematic view of the geometrical configuration is shown

in Fig. 2. The annular region is composed of two cylindrical

bodies with inner cylinder radius (R1=16mm) and outer

cylinder radius (R2=33.5mm). The axial length of cylinder is

z= 1.5m having radii ratio 0.45, to evaluate the effect of

rotating and non-rotating inner cylinders of two Non-

Newtonian fluids on their pressure drop, CFD simulations

were done. Velocity and constant pressure boundary

conditions of the fluid were imposed on the inlet and outlet of

the annulus. No-slip boundary conditions were used at the

inner and outer cylinders. The rotational speed of the inner

cylinder was 0 and 300rpm. An axial velocity of 0.69 m/s

was applied at inlet of the cylinder. The analysis was carried

out in laminar regime. The fluid velocity and pressure drop

for an annulus was calculated for Non-Newtonian fluids to

evaluate their effects on hydrodynamic of annular systems.

Drilling mud shows Non-Newtonian behavior which is

complicated to describe in a simple model. So, proper

selection of rheological model is necessary for calculations to

describe drilling fluid rheology. The rheological data of Non-

Newtonian fluids were best fitted by power law model which

can be expressed as

τ= k (γ) n Eq. (1)

Figure 2: Concentric cylinders with inner shaft rotation

The rheological data of aqueous suspensions of 0.2%

Xanthan Gum (XG) and 0.2% Carboxymethyl-cellulose

(CMC) were measured using a Brookfield rheometer at a

temperature of 25℃ [20], where K is consistency factor, n is

the power law index and τ is shear rate. The power law

parameters have been shown in Table 1 which was obtained

by regression for both fluids using a range of shear rate (γ)

varying from 0 to 80 s-1

to determine the parameters.

Table 1: Parameters of the power law model for the two

fluids Non-Newtonian fluids Parameters of the power law fluid

K[Pa.sn ] n[-] R2

0.2% XG solution 0.678 0.27 0.95

0.2% CMC solution 0.096 0.75 0.94

For an incompressible isothermal laminar fluid flow whose

effective viscosity depends only on strain rate tensor, the

modeling of flow can be defined by continuity equation (Eq.

(2)), using axial, radial and tangential components of the

momentum equation (Eq. (3), (4) and (5)) in cylindrical

coordinates [21].

Eq.(2)

Eq. (3)

Eq. (4)

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 2





Eq. (5)

Considering the power law rheological model (Eq. 1)), we

used the effective viscosity (μE) concept to replace the

dynamic viscosity (μ) in these equations. The parameters of

this model (Table 1) were inserted in FLUENT 15 software.

3. Numerical Simulation

The procedure for the numerical simulation was

implemented using ANSYS FLUENT 15. Finite volume

numerical scheme in FLUENT were employed for solving

mathematical model. In FLUENT, the standard SIMPLE and

SIMPLEC (SIMPLE Consistent) algorithm are available in

solution methods. Simple is the default but SimpleC is more

beneficial for relatively less complicated problems. Here, the

simulations were performed in steady state regime, with

convergence criteria of 1e-4

and SIMPLE algorithm was used

for coupling pressure-velocity. PRESTO scheme was used

for pressure discretization and the scheme QUICK for the

discretization of equations of motion. The boundary

conditions adopted were an axial velocity of 0.69 m/s at

entrance and rotational speeds of 0 and 300 rpm in

concentric channel of inner cylinder.

3.1 Grid Independence Study

Grid construction was also done in ANSYS Fluent software.

In construction of grid, the cells adjacent to the walls of the

inner and outer tubes, as well as in the regions of entry and

exit were refined by mapped face meshing with a cells

growth factor of 1.1. A grid independence test was

performed in which the initial grid elements of 15520 were

considered and subsequently the values were raised to

154400 and 192000 respectively. The final mesh of 192000

cells was chosen as it gave a grid-independent solution.

Figures 3 and 4 showed the refinement of grid along the

annular section and in the entry

region of concentric annuli respectively.

Figure 3: Grid refinement Figure 4: Grid refinement

along concentric annular in intake region section

4. Results and Discussions

4.1 Effects of inner cylinder rotation on pressure drop of

Non- Newtonian fluids

In order to validate the present work, numerical studies were

simulated and the results obtained were compared with the

existing results of those studies. The results obtained from

the simulation for pressure drop in non-Newtonian fluids XG

and CMC are shown in Table 2 and Fig.5. The results were

also compared to both simulated and experimental data

reported in the literature [19]. The difference in data might

be due to following of grid construction with maximum

refinement in ANSYS FLUENT. The results obtained in the

Fluent were taken and plotted in software OriginPro 8.

In the present study, % reduction in pressure drop due to

change in rotational speed of simulated values were found

4.0 & 1.16 against the Non-Newtonian fluids XG and CMC

respectively. But the simulated values for the same Non-

Newtonian fluids were calculated as 4.1 & 1.2 respectively

which were already recorded in literature [19]. However, the

former values found from present study were more nearer to

the experimental and simulated values and seemed to be

more precise and acceptable than reported earlier by

previous workers. So the results from present study showed

that on increase in pipe rotation for same inlet velocity led

to decrease in pressure drop as listed in Table 2.

Figure 5: Comparison of Experimental pressure drop,

simulated and present work simulated values in concentric

annulus: (a) 0.2% XG (b) 0.2% CMC

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 3





Table 2: Pressure drop for XG and CMC obtained from present study compared with those reported in literature

Particulars Rotational

Speed(rpm)

Published

Present work

Simulated

% reduction in

pressure drop due to

change in rotational

speed of present

simulated values

Experimental

% reduction in pressure

drop due to change in

rotational speed of

experimental values

Simulated

% reduction in pressure

drop due to change in

rotational speed of

simulated values

0.2% XG

solution

0 865 3.87

933 4.1

923 4.0

300 831.5 894 886

0.2% CMC

solution

0 1337 1.12

1648 1.2

1639 1.16

300 1322 1628 1620

4.2 Effect of inner cylinder rotation on flow

characteristics of Non- Newtonian fluids

In this section, the numerical results of fluid flow

characteristics for two Non-Newtonian fluids (0.2% XG and

0.2% CMC) with and without inner cylinder rotation cases

were reported. Velocity vectors and contour along with

pressure contour at different rotational speed (0rpm and

300rpm) were presented. Practically, the flow of drilling

fluid is highly affected by drag particles accumulated after

drilling which is determined by velocity profiles in annular

region [2]. So, it becomes necessary to determine velocity

profiles in annular region for efficient drilling operations.

In Fig.6 (a) the maximum velocity of XG was located at the

centerline in the annulus of concentric cylinders without

inner shaft rotation and it showed a non-parabolic profile.

This happened due to pseudoplastic nature of this fluid

having power index n=0.27. Fig. 6 (b) indicated velocity

contours that showed maximum velocity was located at

centerline in annulus of concentric cylinder without inner

shaft rotation. Again in Fig. 7 (a) the velocity increased

towards the inner part of the gap as the inner cylinder rotated

at 300 rpm and Fig. 7 (b) showed the corresponding velocity

contour that indicated that maximum velocity increased near

inner shaft due to rotational speed.

Figure 6: (a) Velocity vector of XG without inner shaft

rotation

Figure 6: (b) Velocity contour for XG (0rpm)

Figure 7: (a) Velocity vector of XG with inner shaft rotation

at 300 rpm

Figure 7: (b) Velocity contour for XG (300rpm)

The pressure decreased at outlet of the cylinders in Fig. 8 (a)

whereas in Fig. 8 (b) with shaft rotation, the pressure

decreased more rapidly at the outlet.

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 4





Figure 8: (a) Pressure contour of XG without inner shaft

rotation

Figure 8: (b) Pressure contour of XG with inner shaft

rotation at 300 rpm

In Fig 9 (a) the maximum velocity was located at centreline

of annulus. It showed almost parabolic profile as CMC has

power law index, n=0.75, which was closer to Newtonian

fluid (n=1). Velocity contour for CMC in concentric

cylinder without inner shaft rotation was shown in Fig. 9 (b).

Again in Fig. 10 (a) and 10 (b), the velocity vector and

contour indicated that the maximum velocity increased

towards the inner part as the cylinder rotated at 300 rpm.

Figure 9: (a) Velocity vector of CMC (0rpm)

Figure 9: (b) Velocity contour of CMC (0rpm)

Figure 10: (a) Velocity vector of CMC with shaft rotation at

300 rpm

Figure 10: (b) Velocity contour of CMC (300 rpm)

In Fig.11 (a) the pressure decreased at outlet of the cylinders

and whereas Fig 11 (b) indicated that with shaft rotation, the

pressure decreased more rapidly at the outlet.

Figure 11: (a) Pressure contour of CMC without inner

shaft rotation

Figure 11: (b) Pressure contour of CMC with inner shaft

rotation at 300 rpm

4.3 Effect of inner cylinder rotation on Axial and

Tangential Velocities of Non- Newtonian fluids

In this section, the numerical results of axial and tangential

velocities for two Non-Newtonian fluids (0.2% XG and 0.2%

CMC) with and without inner cylinder rotation cases were

reported and compared. The simulated profiles of axial and

tangential velocities were presented and compared with the

profiles of [19].

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 5





In Figure 12 (b) profiles of axial velocities were almost

similar to simulated profiles reported in the literature for

both the fluids in Figure 12 (a). Distances were normalized

by radial distance r1 to S from outer to inner cylinder and

velocity was normalized by bulk velocity Ub (0.69m/s).

Significant differences could be seen in profiles normalized

axial velocities and it was noted due to the rheological

characters of the fluids.

The 0.2% CMC solution presented a parabolic profile as it

has a behavior index (n=0.75) very close to Newtonian fluid

(n=1).But, 0.2% XG solution having low behavior index

(n=0.27) displays a flattened profile. It was also seen that the

effect of rotation of inner shaft (300 rpm) did not influence

the axial velocity profiles as shown in the Figure 12.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

u/U

b

r1/S

0.2% XG (0rpm)

0.2% XG (300 rpm)

0.2% CMC (0 rpm)

0.2% CMC (300 rpm)

Figure 12: (a) Simulated profiles of axial velocity

reported in literature.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

u/U

b

r1/S

0.2% XG (0rpm)

0.2% XG (300rpm)

0.2% CMC (0rpm)

0.2% CMC (300rpm)

Figure 12: (b) Simulated profiles of axial of present work

Fig.12. Validation of axial velocity profiles normalised by

bulk velocity (Ub ) for fluids (0.2% XG and 0.2 % CMC)

in concentric annulus

In Figure 13, present study showed almost same tangential

velocity profiles as simulated values reported in literature

[19]. In 0.2% XG solution, the tangential velocity decreased

sharply as fluid moved away from the inner cylinder as its

non-Newtonian behavior was more evident. In contrast

against 0.2% CMC, tangential velocity decreased gradually.

Figure 13: Validation of simulated and present work

tangential velocity profiles normalised by bulk velocity (Ub)

for fluids (0.2% XG and 0.2 % CMC) in concentric annulus.

4.4 Effects of Inner cylinder rotation on pressure drop of

Newtonian fluid

In this section, for further validation, the work was extended

for studying flow characteristics in concentric annuli using

Newtonian fluid. Water was taken here as Newtonian fluid

for analysis. Considering same parameters and boundary

conditions, the results obtained after simulation were

analyzed below and were compared to the results obtained

for the two non-Newtonian fluids (XG and CMC) as shown

in Table 3.

It was noted that the pressure drop for water reduced slightly

to the tune of 2.9% (Fig.14), which might be due to

introduction of inner cylinder rotation (300rpm). By

comparison, it was found that pressure drop varied with

different fluids flowing through the annulus of rotating

cylinders. This was due to differences in behavior of fluids

having power index varying from n=0.27 to n=1 (Table 1).

Table 3: Comparisons of pressure drop for 0.2% XG, 0.2%

CMC and water due to change in rotational speed

Rotational speed (RPM) Particulars

0.2% XG 0.2% CMC Water

0 923 1639 1710

300 886 1620 1660

% reduction in pressure drop 4.0 1.16 2.9

Figure 14: Comparison of pressure drop for both Newtonian

and Non-Newtonian fluids

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 6





In this section, the numerical results of fluid flow

characteristics for Newtonian fluid (Water) with and without

inner cylinder rotation cases were reported. The velocity

vectors, velocity contour and pressure contour for water were

presented here.

In Fig. 15 the maximum velocity without shaft rotation was

located at centerline of annulus in concentric cylinders. The

profile is parabolic in nature as water has power law index

n=1.

The velocity contour as well was shown in Fig. 16. But with

shaft rotation at 300 rpm, the maximum velocity occurred

near the inner rotating cylinder as shown in Fig. 17 and Fig.

18 respectively.

Figure 15: Velocity vectors without inner shaft rotation

(Water)

Figure 16: Velocity contour of Water (0rpm)

Figure 17: Velocity vectors with inner shaft rotation at

300 rpm (Water)

Figure 18: Velocity contour of Water (300 rpm)

In, Fig. 19 (a) the pressure decreased at outlet of the

cylinders but Fig 19 (b) indicated that with shaft rotation, the

pressure decreased more rapidly at the outlet.

Figure 19: (a) Pressure contour of Water (0rpm)

Figure 19: (b) Pressure contour of Water (300rpm)

4.6 Effects of inner cylinder rotation on axial and

tangential velocities of Newtonian fluid

In this section, the numerical results of axial and tangential

velocities for Newtonian fluid (Water) with and without

inner cylinder rotation cases were reported. The simulated

profiles of axial and tangential velocities were presented and

compared with the two Non-Newtonian fluids (0.2% XG and

0.2% CMC).

In Figure 20, it was seen that water gives a parabolic velocity

profile as its power law index is n=1 as compared to XG

having a flat profile (n=0.27) and CMC with almost

parabolic profile (n=0.75).

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 7





Moreover, increment in shaft rotation (300rpm) practically

did not interfere in the axial velocity profiles. The

differences in profiles of three fluids were due to its

rheological characteristics.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

u/U

b

r1/S

0.2% XG(0rpm)

0.2% XG(300rpm)

0.2% CMC(0rpm)

0.2% CMC(300rpm)

Water (0rpm)

Water (300rpm)

Figure 20: Comparison of axial velocities for both

Newtonian and non-Newtonian fluids

In Figure 21, the tangential velocity of water decreased

gradually but there was sharp decrease in tangential velocity

against Non-Newtonian fluids particularly XG. From

comparison with the non-Newtonian fluids, it could be noted

that the velocity gradient of the Newtonian fluid was greater

than that of Non-Newtonian fluid.

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

0.0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

w/U

b

r1/S

0.2% XG (300 rpm)

0.2% CMC (300rpm)

Water (300 rpm)

Figure 21: Comparison of tangential velocity both

Newtonian and Non-Newtonian fluids

5. Conclusion

The present study revealed the following outcomes of the

investigation:

1) The simulated results of present study of the two fluids

showed a decrease in pressure drop with inner cylinder

rotation in the concentric annulus. The pressure drop after

comparison showed nearest values to experimental values

as well better results than simulated values reported in

literature [19]. Hence, it was inferred that the

computation for pressure drop was almost accurate and

validated using ANSYS Fluent 15.

2) The present simulated results showed that the axial

velocities in the concentric annulus were flat for XG

solution and parabolic for CMC solution. But, the

influences of inner shaft rotation on the profiles were

negligible. Again, the tangential velocity profiles

showed a sudden decrease in tangential velocity of XG

solution as it moved away from the inner cylinder, while

this decrease was more gradual with the CMC solution.

The velocities after comparison showed similar profiles

to simulated velocities collected from the literature.

Hence, it was in good conformity with the previous work

cited in literature.

3) To accumulate more information and precise data, the

current study was extended to Newtonian fluid and

compared with the two non-Newtonian fluids. The study

revealed that the pressure drop for water reduced slightly

(reduction of 2.9%) due to introduction of inner cylinder

rotation (300rpm). After comparison, it was computed

that pressure drop varied with different fluids flowing

through the annulus of rotating cylinders. This was due to

differences in behavior of fluids all having power index

varying from n=0.27 to n=1. The property of Newtonian

Fluid (n=1) was substantiated in the present investigation.

4) For axial velocities water gave a parabolic velocity

profile as its power law index is n=1 as compared to XG

having a flat profile (n=0.27) and CMC with almost

parabolic profile (n=0.75). Moreover, increment in shaft

rotation (300rpm) practically did not interfere in the axial

velocity profiles. The differences in profiles of three

fluids were found due to their variable rheological

characteristics.

5) The tangential velocity for water decreased gradually but

there was sharp decrease in tangential velocity against

Non-Newtonian fluids particularly XG. From comparison

with the Non-Newtonian fluids, it was found that the

velocity gradient of the Newtonian fluid was greater than

that of Non-Newtonian fluid.

Finally, it was inferred that the results obtained from present

study were more nearer to the values obtained by the

previous workers and hence more reliable. The extended

work also helped in differencing the rheological

characteristics of various fluids which has effects on

hydrodynamics of annular systems.

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Author Profile

Mehtaj Ridwana Sahin is currently working in

Jorhat Polytechnic as Lecturer in Mechanical

(Automobile Deptt.), Jorhat. Assam. She did her

Master's degree in Mechanical Engineering with area

of specialization in Thermo-Fluid from NERIST, Nirjuli, Arunachal

Pradesh in 2017, graduated from Dibrugarh University, Dibrugarh,

Assam in 2014.

Paper ID: SR20729013358 DOI: 10.21275/SR20729013358 9

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Fluid Flow Analysis in a Concentric Annulus with a